The Dirac equation is the foundation of quantum electrodynamics (QED) which explains the origin of anti-particles. The solution of the Dirac equation represents the relativistic spin-\(\frac{1}{2}\)  fermions and anti-fermions [1]}, [2]}. The Dirac equation can be obtained by minimizing the free QED action (in natural units) [3]}, [4]}, [2]},
\(S = \int d^4 x \bigg (-\frac{1}{4}F_{\mu \nu }F^{\mu \nu } + i \bar{\psi } \gamma ^\mu \partial _{\mu }\psi - m \bar{\psi }\psi \bigg ) \,,\) 
